Growth of large aluminum nitride single crystals with thermal-gradient control

ABSTRACT

In various embodiments, non-zero thermal gradients are formed within a growth chamber both substantially parallel and substantially perpendicular to the growth direction during formation of semiconductor crystals, where the ratio of the two thermal gradients (parallel to perpendicular) is less than 10, by, e.g., arrangement of thermal shields outside of the growth chamber.

RELATED APPLICATION

This application claims the benefit of and priority to U.S. ProvisionalPatent Application No. 61/360,142, filed Jun. 30, 2010, the entiredisclosure of which is hereby incorporated herein by reference.

GOVERNMENT SUPPORT

This invention was made with United States Government support undercontract number DE-FC26-08-NT01578 awarded by the Department of Energy(DOE). The United States Government has certain rights in the invention.

FIELD OF THE INVENTION

In various embodiments, the present invention relates to systems andmethods for fabricating nitride-based crystals, in particular systemsand methods featuring enhanced control over the axial and radial thermalgradients during crystal growth.

BACKGROUND

Aluminum nitride (AlN) holds great promise as a semiconductor materialfor numerous applications, e.g., optoelectronic devices such asshort-wavelength light-emitting diodes (LEDs) and lasers, dielectriclayers in optical storage media, electronic substrates, and chipcarriers where high thermal conductivity is essential, among manyothers. In principle, the properties of AlN may allow light emission atwavelengths down to around 200 nanometers (nm) to be achieved. Recentwork has demonstrated that ultraviolet (UV) LEDs have superiorperformance when fabricated on low-defect AlN substrates prepared frombulk AlN single crystals. The use of AlN substrates is also expected toimprove high-power radio-frequency (RF) devices made with nitridesemiconductors due to the high thermal conductivity with low electricalconductivity. However, the commercial feasibility of AlN-basedsemiconductor devices is limited by the scarcity and high cost of large,low-defect single crystals of AlN.

To make large-diameter AlN substrates more readily available andcost-effective, and to make the devices built thereon commerciallyfeasible, it is desirable to grow large-diameter (>25 mm) AlN bulkcrystals at a high growth rate (>0.5 mm/hr) while preserving crystalquality. The most effective method of growing AlN bulk single crystalsis the “sublimation-recondensation” method that involves sublimation oflower-quality (typically polycrystalline) AlN source material andrecondensation of the resulting vapor to form the single-crystal AlN.U.S. Pat. No. 6,770,135 (the '135 patent), U.S. Pat. No. 7,638,346 (the'346 patent), and U.S. Pat. No. 7,776,153 (the '153 patent), the entiredisclosures of which are incorporated by reference herein, describevarious aspects of sublimation-recondensation growth of AlN, both seededand unseeded. While these references recognize the benefits of a largeaxial (i.e., parallel to the primary growth direction) thermal gradientfor optimizing material quality and growth rate of the growing AlNcrystal, they utilize a growth apparatus designed to minimize the radial(i.e., perpendicular to the primary growth direction) thermal gradient.For example, axial thermal gradients may range from approximately 5°C./cm to approximately 100° C./cm, while radial thermal gradients aremaintained at as negligible a level as possible. Likewise, otherprior-art growth apparatuses utilize heavy insulation in order tominimize or eliminate the radial thermal gradient, as a minimized radialthermal gradient is expected to produce flat, high-quality crystals,particularly when efforts are made to grow crystals having largediameters. The radial gradient is typically minimized duringconventional crystal growth in order to prevent formation of defectssuch as dislocations and low-angle grain boundaries. It is alsominimized to make the surface of the growing crystal more flat, thusincreasing the amount of usable material in the crystal (i.e.,increasing the number of substrates that can be cut from the crystal fora given length of crystal).

FIG. 1 depicts an apparatus 100 utilized for the growth of AlN inaccordance with the above-described prior art. As shown, a crucible 105is positioned on top of a crucible stand 110 within a cylindricalsusceptor 115. During the growth process, the susceptor 115 istranslated within a heated zone created by surrounding heating coils(not shown), polycrystalline AlN source material 120 at the base 125 ofthe crucible sublimes at the elevated temperature, and the resultingvapor recondenses at the cooler tip 130 of the crucible due to the largeaxial thermal gradient between the base 125 and the tip 130, thusforming an AlN crystal 135. The apparatus 100 also features top axialshields 140 and bottom axial shields 145 designed and positioned tominimize the radial thermal gradient perpendicular to the growthdirection 150 of AlN crystal 135. As shown, the tip 130 of the crucible105 is cooler than the base 125 at least in part because apparatus 100has fewer top axial shields 140 than bottom axial shields 145, allowingmore heat to escape in the region of tip 130 and generating the desiredaxial thermal gradient. The top axial shields 140 may have centeredholes therewithin to facilitate measurement of the temperature at tip130 by a pyrometer 155. The centered hole diameter is minimized toreduce the heat flow but sufficient to form a practical optical path forthe temperature sampling by the pyrometer 155. Additional pyrometers160, 165 may also be utilized to measure temperatures at other regionsof apparatus 100.

As mentioned above, the ability to grow AlN single crystals at highgrowth rates would spur additional commercial adoption of thetechnology. While increasing the growth rate of AlN crystals istheoretically possible by increasing the Al supersaturation using largeraxial thermal gradients, increases in the Al supersaturation may resultin deterioration of the material quality of the crystal, or even inpolycrystalline, rather than single-crystal, growth. Furthermore, theminimization or elimination of radial thermal gradients during AlNcrystal growth unexpectedly tends to deleteriously impact the quality ofthe AlN crystal, particularly when attempts are made to grow large(e.g., >25 mm diameter) crystals at reasonable growth rates (e.g., >0.5mm/hr). Thus, a need exists for systems and techniques enabling growthof such large AlN crystals at high growth rates while still preservinghigh material quality of the AlN crystal.

SUMMARY

Embodiments of the current invention achieve high growth rates (e.g.,greater than approximately 0.5 mm/hr) of large, high-qualitysingle-crystal semiconductors (e.g., AlN) by forming and maintainingnon-zero axial and radial thermal gradients in the growth apparatus suchthat the ratio of the axial thermal gradient to the radial thermalgradient (the “thermal gradient ratio”) is greater than zero and lessthan 10. (As utilized herein, a thermal gradient being maintained doesnot necessarily imply that it is held constant as a function of time,only that it is non-zero (and constant or fluctuating) over a period oftime.) The size and the quality of growing crystals are generallyinfluenced by the thermal field within the growth cell. The axialthermal gradient is the magnitude of the thermal field projected on thelongitudinal symmetry axis in a cylindrical coordinate system. Theradial thermal gradient is the projection of the thermal field magnitudeon the azimuthal direction. Therefore, the thermal gradient in any otherdirection may be described as a superposition of the axial and radialthermal gradients (and thus may also be controlled as the axial and/orradial thermal gradients are controlled). The deliberate formation andcontrol of the radial thermal gradient large enough to result in athermal gradient ratio less than 10 contradicts the above-describedconventional wisdom in which radial thermal gradients (which may dependat least in part on the dimensions and shape of the growth chamber),even if formed at all (e.g., unintentionally) are eliminated orminimized to small magnitudes.

In some embodiments, the radial thermal gradient and the axial thermalgradient are substantially balanced and, preferably, the thermalgradient ratio ranges from approximately 1.2 to approximately 5.5. Inorder to facilitate formation and control of the radial thermalgradients, crystal-growth apparatuses in accordance with variousembodiments of the invention utilize different types, thicknesses,and/or arrangements of thermal shields, particularly in the area“behind” the growing crystal (i.e., corresponding to the location of thetop axial shields 140 in FIG. 1). Thus, for embodiments featuring seededgrowth of AlN single crystals, one or more shields are typically locatedopposite the growth surface of the seed. The one or more shieldsutilized in preferred embodiments of the invention include or consistessentially of one or more refractory materials, e.g., tungsten, and maybe substantially thin, i.e., have thicknesses less than 0.5 mm, e.g.,ranging from 0.125 mm to 0.5 mm.

In one aspect, embodiments of the invention feature a method of formingsingle-crystal aluminum nitride (AlN). Vapor comprising or consistingessentially of aluminum and nitrogen is condensed within a growthchamber, thereby forming an AlN single crystal that increases in sizealong a growth direction. During the formation, a first (e.g., axial)non-zero thermal gradient is formed and maintained within the growthchamber in a direction substantially parallel to the growth direction,and a second (e.g., radial) non-zero thermal gradient is formed andmaintained within the growth chamber in a direction substantiallyperpendicular to the growth direction. The ratio of the first thermalgradient to the second thermal gradient is less than 10.

Embodiments of the invention may include one or more of the following inany of a variety of combinations. Solid source material (which mayinclude or consist essentially of, e.g., polycrystalline AlN) may besublimed within the growth chamber to form the vapor. The second thermalgradient may be larger than 4° C./cm and/or smaller than 85° C./cm. Theratio of the first thermal gradient to the second thermal gradient maybe greater than 1.2. The first thermal gradient may be larger than 5°C./cm and/or smaller than 100° C./cm. The ratio of the first thermalgradient to the second thermal gradient may be less than 5.5, or evenless than 3.

Forming the second thermal gradient may include or consist essentiallyof arranging a plurality of thermal shields outside the growth chamber.Each of the thermal shields may include or consist essentially of arefractory material, e.g., tungsten. Each thermal shield may define anopening therethrough. The openings of the thermal shields may besubstantially equal in size to each other. The opening of each thermalshield may range from approximately 10 mm to approximately 2 mm lessthan the dimension of the growth chamber substantially perpendicular tothe growth direction. The openings of at least two of the thermalshields may be different in size. A first thermal shield having a firstopening may be disposed between the growth chamber and a second thermalshield, the second thermal shield having a second opening larger thanthe first opening. At least two of the thermal shields may havedifferent thicknesses. The thickness of each of the thermal shields mayrange from approximately 0.125 mm to approximately 0.5 mm.

The growth chamber may include a lid disposed between the AlN singlecrystal and at least one (or even all) of the thermal shields. Thethickness of the lid may be less than approximately 0.5 mm. The lid mayinclude or consist essentially of tungsten. A seed may be disposedwithin the growth chamber before forming the AlN single crystal, and theAlN single crystal may form on the seed and extend therefrom in thegrowth direction. The diameter of the seed may be greater thanapproximately 25 mm. The growth rate of the AlN single crystal may begreater than approximately 0.5 mm/hr. The AlN single crystal may form ona seed disposed within the growth chamber.

In another aspect, embodiments of the invention feature a crystal-growthsystem including or consisting essentially of a growth chamber for theformation of a single-crystal semiconductor material viasublimation-recondensation therewithin along a growth direction, aheating apparatus for heating the growth chamber, and a plurality ofthermal shields arranged to form, within the growth chamber, (i) a firstnon-zero thermal gradient in a direction substantially parallel to thegrowth direction and (ii) a second non-zero thermal gradient in adirection substantially perpendicular to the growth direction. The ratioof the first thermal gradient to the second thermal gradient is lessthan 10.

Embodiments of the invention may include one or more of the following inany of a variety of combinations. Each thermal shield may define anopening therethrough. The openings of at least two of the thermalshields may be different in size. A first thermal shield having a firstopening may be disposed between the growth chamber and a second thermalshield, the second thermal shield having a second opening larger thanthe first opening. At least two of the thermal shields may havedifferent thicknesses. The thickness of each of the thermal shields mayrange from approximately 0.125 mm to approximately 0.5 mm. Each of thethermal shields may include or consist essentially of a refractorymaterial, e.g., tungsten. The thermal shields may be arranged withsubstantially equal spacings therebetween. A seed for nucleating thesingle-crystal semiconductor material thereon may be disposed within thegrowth chamber. The diameter of the seed may be greater thanapproximately 25 mm, and/or the seed may include or consist essentiallyof aluminum nitride. The ratio of the first thermal gradient to thesecond thermal gradient may be less than 5.5, or even less than 3. Theratio of the first thermal gradient to the second thermal gradient maybe greater than 1.2.

These and other objects, along with advantages and features of theinvention, will become more apparent through reference to the followingdescription, the accompanying drawings, and the claims. Furthermore, itis to be understood that the features of the various embodimentsdescribed herein are not mutually exclusive and can exist in variouscombinations and permutations. Unless otherwise indicated, “radial”generally refers to a direction substantially perpendicular to theprimary crystal growth direction and/or the long axis of the crystaland/or the crystal-growth apparatus. Refractory materials are generallymaterials that are physically and chemically stable at temperaturesabove approximately 500° C. As used herein, the term “substantially”means ±10%, and, in some embodiments, ±5%. The term “consistsessentially of” means excluding other materials that contribute tofunction, unless otherwise defined herein. Nonetheless, such othermaterials may be present, collectively or individually, in traceamounts.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, like reference characters generally refer to the sameparts throughout the different views. Also, the drawings are notnecessarily to scale, emphasis instead generally being placed uponillustrating the principles of the invention. In the followingdescription, various embodiments of the present invention are describedwith reference to the following drawings, in which:

FIG. 1 is a schematic cross-section of a crystal-growth apparatus inaccordance with the prior art in which radial thermal gradients areminimized or eliminated;

FIG. 2 is a schematic cross-section of a crystal-growth apparatus inaccordance with various embodiments of the invention in which radialthermal gradients are generated and/or controlled;

FIGS. 3A and 3B are schematic cross-sections of portions of thecrystal-growth apparatus of FIG. 2 with alternate arrangements of topthermal shields, in accordance with various embodiments of theinvention; and

FIG. 4 is a table listing various steps of a process for growth ofsemiconductor crystals such as AlN in accordance with variousembodiments of the invention.

DETAILED DESCRIPTION

FIG. 2 depicts a crystal-growth apparatus 200 suitable for the growth ofsingle-crystal semiconductor materials (e.g., AlN, Al_(x)Ga_(1-x)N,B_(x)Al_(1-x)N, and/or B_(x)Ga_(y)Al_(1-x-y)N) in accordance withvarious embodiments of the present invention. As shown, apparatus 200includes a crucible 205 positioned on top of a crucible stand 210 withina susceptor 215. Both the crucible 205 and the susceptor 215 may haveany suitable geometric shape, e.g., cylindrical. During a typical growthprocess, the semiconductor crystal 220 is formed by condensation of avapor 225 that includes or consists essentially of the elemental and/orcompound precursors of the semiconductor crystal 220. For example, for asemiconductor crystal 220 including or consisting essentially of AlN,vapor 225 may include or consist essentially of Al and N atoms and/or N₂molecules. In preferred embodiments, the vapor 225 arises from thesublimation of a source material 230, which may include or consistessentially of the same material as semiconductor crystal 220, only inpolycrystalline form. Source material 230 may be substantially undopedor doped with one or more dopants, and use of a doped source material230 typically results in semiconductor crystal 220 incorporating thedopant(s) present in source material 230. The semiconductor crystal 220may form on and extend from a seed crystal 235. (Alternatively, thesemiconductor crystal 220 may nucleate upon and extend from a portion ofthe crucible 205 itself, in the manner depicted in FIG. 1.) The seedcrystal 235 may be a single crystal (e.g., a polished wafer) includingor consisting essentially of the same material as semiconductor crystal220 or may be a different material.

The crucible 205 may include or consist essentially of one or morerefractory materials, such as tungsten, rhenium, and/or tantalumnitride. As described in the '135 patent and the '153 patent, thecrucible 205 may have one or more surfaces (e.g., walls) configured toselectively permit the diffusion of nitrogen therethrough andselectively prevent the diffusion of aluminum therethrough.

As shown in FIG. 2, during formation of the semiconductor crystal 220, apolycrystalline material 240 may form at one or more locations withinthe crucible 205 not covered by the seed crystal 235. However, thediameter (or other radial dimension) of the semiconductor crystal 220may expand, i.e., increase, during formation of the semiconductorcrystal 220, thereby occluding the regions of polycrystalline material240 from impinging vapor 225 and substantially limiting or eveneliminating their growth. As shown in FIG. 2, the diameter of thesemiconductor crystal 220 may expand to (or even start out at, inembodiments utilizing larger seed crystals 235) be substantially equalto the inner diameter of the crucible 205 (in which case no furtherlateral expansion of the semiconductor crystal 220 may occur).

The growth of the semiconductor crystal 220 along a growth direction 245typically proceeds due to a relatively large axial thermal gradient(e.g., ranging from approximately 5° C./cm to approximately 100° C./cm)formed within the crucible 205. A heating apparatus (not shown in FIG. 2for clarity), e.g., an RF heater, one or more heating coils, and/orother heating elements or furnaces, heats the susceptor 215 (and hencethe crucible 205) to an elevated temperature typically ranging betweenapproximately 1800° C. and approximately 2300° C. The apparatus 200features one or more sets of top thermal shields 250, as well as one ormore sets of bottom axial thermal shields 255, arranged to create thelarge axial thermal gradient (by, e.g., better insulating the bottom endof crucible 205 and the source material 230 from heat loss than the topend of crucible 205 and the growing semiconductor crystal 220). Duringthe growth process, the susceptor 215 (and hence the crucible 205) maybe translated within the heating zone created by the heating apparatusvia a drive mechanism 260 in order to maintain the axial thermalgradient near the surface of the growing semiconductor crystal 220. Oneor more pyrometers 265 (or other characterization devices and/orsensors) may be utilized to monitor the temperature at one or morelocations within susceptor 215. The top thermal shields 250 and/or thebottom thermal shields 255 may include or consist of one or morerefractory materials (e.g., tungsten), and are preferably quite thin(e.g., between approximately 0.125 mm and 0.5 mm thick).

As mentioned above, the maximum mass transfer from source material 230and/or vapor 225 (and therefore growth rate of semiconductor crystal220) is typically achieved by maximizing the axial thermal gradientwithin the crucible 205 (i.e., maximizing the temperature differencebetween the source material 230 and the growing crystal 220 so that thegrowing crystal 220 has greater supersaturation). In preferredembodiments, the onset of crystal-quality deterioration (e.g., increaseddislocation density, formation of grain boundaries, and/orpolycrystalline growth) sets the approximate upper limit of thesupersaturation at a given growth temperature. For typical growthtemperatures (e.g., between approximately 2125° C. and approximately2275° C.), this upper limit of the axial temperature gradient isgenerally approximately 100° C./cm (although this maximum may depend atleast in part on the dimensions and/or shape of the growth chamber, andmay thus be larger for some systems). However, as the cross-sectionalarea of the semiconductor crystal 220 increases (and/or for larger-areaseed crystals 235), the probability of parasitic nucleation (on the seedcrystal 235 or in other locations) increases. Each parasitic nucleationevent may lead to formation of an additional growth center and result ingrain or sub-grain formation (and thus low-quality and/orpolycrystalline material). Minimizing the probability of parasiticnucleation is preferably achieved by providing a non-zero radial thermalgradient in a direction substantially perpendicular to the growthdirection 245 that promotes lateral growth. Formation of the radialthermal gradient also enables growth of larger, high-quality crystals athigh growth rates, as previously mentioned.

In accordance with various embodiments of the invention, the top thermalshields 250 are also arranged to form the non-zero radial thermalgradient within crucible 205. The radial thermal gradient is preferablylarger than 4° C./cm, e.g., ranging between 4° C./cm and 85° C./cm(although, as described above relative to the axial thermal gradient,these values may depend on the specific dimensions and/or shape of thecrucible). In preferred embodiments, the axial and radial temperaturegradients are balanced. The radial and axial thermal gradients arebalanced when the magnitudes of the gradients are within their upperlimits (as detailed below). Preferably, the ratio between the axial andradial gradients (the thermal gradient ratio) is less than 10, less than5.5, or even less than 3 at any given point inside the crucible 205. Thethermal gradient ratio is also preferably greater than 1.2, e.g.,ranging from 1.2 to 5.5. The maximum (i.e., upper limit) radialtemperature gradient is a function of the growth temperature and ispreferably defined by the onset of cracking and/or increased dislocationdensity (and/or grain-boundary formation) in semiconductor crystal 220.At the growth temperature, dislocation arrays, or even grain boundaries,may form at elevated radial thermal gradients. Such defects usuallyexhibit center-symmetric patterns. The minimum (i.e., lower limit) ofthe radial thermal gradient is preferably set by complete lack oflateral growth of the semiconductor crystal 220 perpendicular to thegrowth direction 245.

As noted above, after the semiconductor crystal 220 has laterallyexpanded to the inner dimension of the crucible 205 the expansiongenerally ceases. However, preferred embodiments of the inventionmaintain a non-zero radial thermal gradient (which may be different fromthe radial thermal gradient during the expansion of the semiconductorcrystal 220) even after the lateral expansion of semiconductor crystal200 has ceased in order to maintain high crystalline quality. Thenon-zero positive (as defined herein) radial thermal gradient generallyresults in semiconductor crystal 220 having a convex surface duringgrowth (e.g., as shown in FIG. 2). Lateral growth of semiconductorcrystal 220 promotes growth-center coalescence, and preferably growthinitiates and proceeds from only one growth center. Even in such a case,there is preferably some non-zero magnitude of the radial gradient toprevent formation of additional growth centers. Examples of balancedaxial and radial thermal gradients for growth of semiconductor crystalhaving a diameter of approximately two inches are set forth in the tablebelow.

Growth Thermal gradient upper limit (° C./cm) Axial/Radial temperature(° C.) Axial Radial ratio 1800 25 12 2.1 2250 105 45 2.3

In preferred embodiments, the crucible 205 has a lid 270 with sufficientradiation transparency to enable at least partial control of the thermalprofile within the crucible 205 via the arrangement of the top thermalshields 250. Furthermore, in embodiments featuring a seed crystal 235,the seed crystal 235 is typically mounted on the lid 270 prior to thegrowth of semiconductor crystal 220. The lid 270 is typicallymechanically stable at the growth temperature (e.g., up to approximately2300° C.) and preferably substantially prevents diffusion ofAl-containing vapor therethrough. Lid 270 generally includes or consistsessentially of one or more refractory materials (e.g., tungsten,rhenium, and/or tantalum nitride), and is preferably fairly thin (e.g.,less than approximately 0.5 mm thick).

The arrangement of the top thermal shields 250 provides control of theradial thermal profile, and hence provide the radial gradient preferredto maintain high crystal quality at high growth rates and to form andmaintain the desired thermal gradient ratio. Simultaneously, the shieldarrangements provide the necessary heat transfer to ensure the maximumgrowth rate. The balance between the axial and radial thermal gradientsmay be achieved by providing certain opening arrangements of theshields. As shown in FIG. 2, each of the top thermal shields typicallyhas an opening 275 therethrough. The opening 275 normally echoes thegeometry and/or symmetry of the crucible 205 (e.g., the opening 275 maybe substantially circular for a cylindrical crucible 205). The size ofeach opening 275 may be varied; typically, the size(s) range from aminimum of 10 mm to a maximum of approximately 5 mm (or even 2 mm) lessthan the diameter of the crucible 205.

For example, in a preferred embodiment, five thermal shields 250, eachhaving a diameter of 68.5 mm and an opening size (diameter) of 45 mm,are used. The thickness of each of the thermal shields 250 is 0.125 mm,and the thermal shields 250 are spaced approximately 7 mm from eachother. At a typical growth temperature of 2065° C., this shieldarrangement results in a radial thermal gradient (measured from thecenter of the semiconductor crystal to the inner edge of the crucible)of 27° C./cm.

As shown in FIG. 2, the top thermal shields 250 may have openings 275larger than any such opening present in the bottom thermal shields 255,and/or the top thermal shields 250 may be stacked with one or morespacings between shields that are larger than that between the variousbottom thermal shields 255. The spacings may range between approximately1 mm and approximately 20 mm, and preferably between approximately 7 mmand approximately 20 mm. Also as shown, the openings 275 in the topthermal shields 250 may all be substantially equal to each other.Depending upon the desired growth conditions (e.g., pressure,temperature, crucible dimensions, distance between the seed crystal andthe source material, etc.), the number of top thermal shields 250, thespacing between shields 250, and/or the size of the openings 275 may bevaried to form the desired radial thermal gradient and hence, thedesired thermal gradient ratio. The radial thermal gradient may even bevaried in real time during the growth of semiconductor crystal 220,e.g., in response to feedback based on determination of the radialthermal gradient during growth. For example, the radial thermal gradientmay be determined based on the temperatures of lid 270 and one or moresides of crucible 215 (e.g., measured by pyrometers 265 as shown in FIG.2).

Similarly, although each of the top thermal shields 250 preferably has athickness less than 0.5 mm, the thickness of one or more of the shields250 may be varied with respect to the others. For example, one or moretop thermal shields 250 may have a thickness of approximately 0.25 mmwhile one or more others have a thickness of approximately 0.125 mm. Thethickness of the top thermal shields 250 may even be varied as afunction of distance away from the lid 270 (i.e., either increasing ordecreasing). Such thermal shields 250 having different thicknesses maybe utilized to adjust the thermal field above and within the crucible215. For example, a thicker shield may be used to block more radiativeheat flow but will typically have higher thermal impact at temperatureswhere the heat flux is dominated by the thermal conductivity (lowertemperatures, e.g. <1500°-1800°). Therefore, the resultant radialthermal gradient may vary as a function of growth temperature, even withthe same arrangement of the same top thermal shields 250.

FIGS. 3A and 3B depict alternative arrangements of the top thermalshields 250 for producing a radial thermal gradient within crucible 205.Specifically, the openings 275 in the top thermal shields 250 can bevaried as a function of distance away from the lid 270. As shown in FIG.3A, the top thermal shields 250 may be arranged such that their openings275 increase in size with increasing distance from lid 270. FIG. 3Bdepicts an alternate arrangement in which the top thermal shields arearranged such that their openings 275 decrease in size with increasingdistance from lid 270. Of course, either of the arrangements of FIGS. 3Aand 3B may be combined with any of the other arrangement variationsdescribed previously. In some embodiments, the arrangement of FIG. 3A ispreferred, as it increases the probability of forming and maintaining asingle growth center (where the narrowest opening is located) at theinitial stages of growth.

Having described the principles and apparatus of various embodiments ofthe present invention, the method of operation, i.e., a growth processfor AlN using the system described above is now described in conjunctionwith FIG. 4. As listed therein, in some embodiments, crystal growthinitially involves evacuating the susceptor 215 (step 400), e.g., topressures on the order of about 0.01 mbar (1 Pa) using a vacuum pump.The susceptor 215 is then refilled with an inert gas or a gas includingor consisting essentially of nitrogen (step 405). These steps arepreferably repeated one or more times to minimize oxygen and moisturecontamination (step 410). Steps 400-410 may be performed by evacuatingand refilling a process chamber (not shown in FIG. 2) that houses thesusceptor 215 and various other portions of apparatus 200, andreferences to the “chamber” below may refer to such a chamber or to thesusceptor 215. The chamber is then pressurized to about 1 bar (100 kPa)with nitrogen gas which is preferably mixed with a small amount ofhydrogen (step 415). For example, a gas including or consistingessentially of about 95-100% N₂ and 0-5% H₂ is suitable in manyembodiments. In particular embodiments, a commercially-available mixtureof about 3% H₂ and 97% N₂ is employed. Polycrystalline AlN sourcematerial 230 is placed at a proximal end of the crucible 230 (step 420).The crucible 230 may then be evacuated and sealed, or may be providedwith selective openings as described hereinabove. The crucible 230 isthen disposed concentrically within the susceptor 215 with its distalend opposite the source material 230 (at which a seed crystal 235 may bedisposed) in the high-temperature region of the heating zone produced bythe heating apparatus (e.g., a furnace (step 425). The temperature isthen increased to bring the distal end of the crucible 205 to atemperature of approximately 1800° C., in particular embodiments, withinabout 15 minutes (step 430). At the end of this temperature ramp, thegas pressure is set and maintained at a predetermined super-atmosphericpressure (step 435), and the temperature is ramped to a finalcrystal-growth temperature (step 440), e.g., in about 5 hours. Asmentioned above, the final crystal-growth temperature may range betweenapproximately 1800° C. and approximately 2300° C. During the temperatureramp, the pressure may be continuously adjusted, e.g., using a ventvalve (not shown) to maintain it at that fixed super-atmospheric value(step 445). One potential advantage of this ramping is the enhancementof the purity of the source material 230 by permitting part of anyoxygen still contained within it to diffuse out of the crucible 205(e.g., through the crucible walls). This diffusion occurs because thevapor pressure of the aluminum suboxides (such as Al₂O, AlO, etc.)generated due to the presence of oxygen in the source material 230, isknown to be higher than that of Al over AlN for the same temperature.

Once the growth temperature is reached, the drive mechanism 260 isactuated to move the distal end of crucible 205 towards the distal endof the chamber, and relative to the axial thermal gradient produced atleast in part by the heating apparatus and the arrangement of the topand bottom thermal shields (step 450). Preferably, the distal end ofcrucible 205 is initially located within the highest-temperature regionof the susceptor 215 at the beginning of the growth run. As the crucible205 moves upwards the distal end of crucible 205 becomes cooler than thesource material 230, which promotes effective mass transport from thesource material 230 to the colder region of the crucible 205.

During the growth process, the pressure is preferably maintained at aconstant predetermined value (step 455). The most appropriate value forthis pressure typically depends on the axial spacing between the sourcematerial 230 and the (closest) surface of the growing crystal 220, aswell as the rate of nitrogen diffusion through the crucible walls orflow through other openings. It may also be appropriate to activelyadjust the gas pressure over a relatively narrow range during crystalgrowth to compensate for any changes in the spacing between the surfaceof the sublimating source material 230 and the growing crystal surface.

In particular embodiments, a pressure of about 18 psi has been used todemonstrate growth rates of 0.9 mm/hr with a separation between thesource material 230 and the surface of the crystal 220 of approximately2 cm, employing tungsten crucibles fabricated by either chemical vapordeposition or powder metallurgy technique (such as those described incommonly assigned U.S. Pat. No. 6,719,843, the entirety of which isincorporated by reference herein). The source-to-growing-crystal-surfacedistance may vary during the growth run if the area of the growingcrystal surface is different from the surface area of the sourcematerial 230 and the growth rate (i.e., axial rate of movement of thecrucible through the temperature gradient) may be adjusted to accountfor any such change. However, typically the surface area of the sourcematerial 230 and growing crystal surface will be kept nominally constantand approximately the same size so that the separation between thesource and growing crystal surface will remain substantially constantduring most of the growth.

Finally, the movement of crucible 205 is stopped (step 460) and acooling ramp (step 465) is established to bring the apparatus and thecrystal 220 to room temperature. Using pressures in the range 100 kPa to150 kPa (1 atm to 1.5 atm), single-crystal boules have been grown at anaxial pushing rate ranging between about 0.4 and 0.9 mm/h, for example,at the rate of 0.455 mm/h. By adjusting the distance between the sourcematerial and the growing crystal surface, and by adjusting the axial andradial temperature gradients, other useful growth conditions may beobtained. Hence, skilled practitioners may usefully use variousembodiments of the present invention with total chamber pressures from50 kPa to 1 MPa (0.5 atm to 10 atm) and axial pushing/growth rates of0.3 to about 3 mm/h, or even higher.

By slicing or cutting the bulk single crystals of embodiments of thepresent invention, crystalline substrates, e.g., of AlN, of desiredthickness—for example, about 500 μm or 350 μm—may be produced. Thesesubstrates may then be prepared, typically by polishing, forhigh-quality epitaxial growth of appropriate layers of AlN, GaN, InNand/or their binary and tertiary alloys to form electronic andoptoelectronic devices such as UV laser diodes and high-efficiency UVLEDs. The aforementioned nitride layers may be described by the chemicalformula Al_(x)Ga_(y)In_(1-x-y)N, where 0≦x≦1 and 0≦y≦1-x.

In various embodiments, the surface preparation of crystals including orconsisting essentially of AlN enables high-quality epitaxial growth ofnitride layers on the AlN substrate. Surface damage is preferablycarefully removed in order to obtain high-quality epitaxial layersneeded for fabrication of high performance nitride semiconductordevices. One successful approach to remove surface damage from the AlNsubstrate is to employ a chemical-mechanical polishing (CMP) approach,e.g. as described in U.S. Pat. No. 7,037,838 (the '838 patent),incorporated herein by reference in its entirety. Through this approach,very high-quality epitaxial layers of Al_(X)Ga_(y)In_(1-x-y)N with lowdislocation densities may be produced using organometallic vapor phaseepitaxy (OMVPE), particularly when x exceeds 0.5. Those skilled in theart will recognize that other epitaxial growth techniques such asmolecular beam epitaxy (MBE) or hydride vapor phase epitaxy (HVPE) mayalso be successfully employed to produce high-quality epitaxial layerson the high-quality semiconductor crystals produced in accordance withembodiments of the present invention.

The growth of bulk single crystals has been described herein primarilyas being implemented by what is commonly referred to as a “sublimation”or “sublimation-recondensation” technique wherein the source vapor isproduced at least in part when, for production of AlN, crystallinesolids of AlN or other solids or liquids containing AlN, Al or N sublimepreferentially. However, the source vapor may be achieved in whole or inpart by the injection of source gases or like techniques that some wouldrefer to as “high-temperature CVD.” Also, other terms are sometimes usedto describe these and other techniques that are used to grow bulk singleAlN crystals according to this invention. Therefore, the terms“depositing,” “depositing vapor species,” and like terms will sometimesbe used herein to generally cover those techniques by which the crystalmay be grown pursuant to embodiments of this invention.

Thus, the single-crystal semiconductors fabricated using the embodimentsdescribed hereinabove may be used to produce substrates by cutting awafer or cylinder from the bulk single-crystal, preparing a surface onthe wafer or cylinder in a known manner to be receptive to an epitaxiallayer, and depositing an epitaxial layer on the surface usingconventional deposition techniques.

In particular embodiments of the invention, large, e.g. greater thanabout 25 mm in diameter, single-crystal AlN wafers are produced fromsingle-crystal AlN boules having a diameter exceeding the diameter ofthe final substrate, e.g., boules having a diameter greater than about30 mm. Using this approach, after growing the boule and orienting it,e.g. by employing x-ray Laue diffraction technique, to obtain adesirable crystallographic orientation for the wafer, the boule ismechanically ground down to a cylinder having a desirable diameter andthen sliced into individual wafers, e.g., using a wire saw. In someversions of these embodiments, the boules are grown by, first, producinghigh-quality single-crystal seeds, and then using the seed crystals asnuclei to grow larger diameter single-crystal boules through acrystal-expansion growth run. Large-diameter slices from this secondcrystal growth process may then be utilized to grow large-diametercrystals without diameter expansion. In alternative versions, thecrystal growth is self-seeded, i.e. the crystal is grown withoutemploying single-crystal seeds.

In various embodiments, high-purity source material 230 including orconsisting essentially of AlN may be produced in a crucible 205 (orother suitable container) by reacting high-purity Al (e.g. having99.999% purity, available from Alpha Aesar of Ward Hill, Mass., USA)with high-purity N₂ gas (e.g. having 99.999% purity, available fromAwesco of Albany, N.Y., USA). In a particular embodiment, pieces ofhigh-purity AlN ceramic, e.g. weighing about 9 g or less, are placed ina bottom portion of the crucible and heated to about 2300° C. in aforming gas atmosphere in order to sublime the AlN and recondense it. Asa result, the density of the resulting ceramic may be increased toapproximately theoretical density by sublimation transport to decreasethe surface area relative to the volume of the source material. Theresulting AlN ceramic source material 230 may have impurityconcentration of less than about 500 ppm.

In growth processes in accordance with various embodiments of theinvention, the crucible 205 loaded with the source material 230 may beassembled and/or disposed in the heating apparatus, e.g. high-pressurecrystal growth furnace available from Arthur D. Little, Inc.Specifically, the crucible 205 may be placed on crucible stand 210within the susceptor 215. Both top thermal shields 250 and bottomthermal shields 255 may then be installed around the crucible 205 withthe susceptor 215 around the crucible 205 and thermal shields. Thecrucible 205 is preferably positioned such that the lid 270 and/or seedcrystal 235 is either below or above the location of the large axialthermal gradient formed by the thermal shields. In the first case (i.e.below the large axial gradient) the seed crystal 235 is initiallymaintained at a higher temperature than the source material 230 so thatlittle or no nucleation occurs during a warm-up. If the seed crystal 235is above the large axial gradient the initial nucleation is generallycontrolled by modification of the temperature ramp-up profile.

The growth chamber is then closed and evacuated, as described above, toreduce trace atmosphere contamination of the nucleation process and theresulting single crystal. In various embodiments, following evacuation,e.g., to less than about 1 Pa employing a mechanical Welch pump withminimum pressure of about ˜0.5 Pa, the chamber is filled with a forminggas blend of 3% H₂ and 97% N₂ to a pressure of about 100 kPa and thenevacuated again to less than 10 mTorr. This refill and pump process maybe carried out three times or more to reduce chamber contamination.Following the pump and refill processes, the chamber is filled with theforming gas to a pressure of, e.g., 117 kPa. High-purity grade gas,e.g., available from GTS-WELCO (99.999% certified), may be used tofurther ensure a clean growth chamber atmosphere.

During a ramp to the growth temperature, the pressure in the chamberincreases until the target growth pressure of, e.g., 124 kPa is reached.After reaching the operating pressure, the chamber pressure may beperiodically checked and incrementally adjusted by releasing gas fromthe chamber to a vent line in order to keep the chamber pressurebetween, e.g., 124 kPa and 125 kPa.

In some embodiments, the power supply for operating the growth apparatus200 is an RF oscillator with a maximum power output of 75 kW at 10 kHz.The growth temperature inside the heating apparatus may be increased intwo ramp segments. For example, the first segment of the ramp may belinear for about 1.5 hours taking the top axial optical pyrometertemperature to about 1800° C. The second ramp segment may then be linearfor approximately 3.5 hours taking the top axial temperature to about2050° C. The chamber may then be maintained at growth temperature andpressure for a period of about 1 hour. Then, the crucible 205 may bemoved up by the drive apparatus at a rate of, for example, approximately0.5 mm/hr. During the growth run, this push rate is held constant, suchthat the total travel is about 30 mm, producing a single-crystal AlNboule that reached about 35 mm in length and about 50 mm in diameter.Shorter or longer crystals may be produced by varying the traveldistance (which is directly related to the push time). The cool-downfrom growth temperature can be done linearly for the period of timebetween approximately 1 and approximately 24 hours. Once the apparatusis at room temperature, the chamber may be pumped to less than 1 Pa andbackfilled to atmospheric pressure with the forming gas, allowing thechamber to be opened and the growth crucible assembly removed from theheating apparatus for evaluation. The growth chamber may then be closedand evacuated as described above to reduce trace atmospherecontamination of the growth cell, nucleation process and resulting AlNsingle crystal.

In particular embodiments, following pump-down to less than 7 mPa, e.g.,using a turbo pump with a minimum pressure of about 0.4 mPa, the chamberis filled with a forming gas blend of 3% H₂ and 97% N₂ to a pressure ofabout 122 kPa. Following the pump and refill process, the chamber isfilled with the forming gas for the start of the growth process to apressure of 117 kPa. As described above, a high-purity grade gasavailable from GTS-WELCO (99.999% certified) may be used to furtherensure a clean growth chamber atmosphere.

During a ramp to the growth temperature, the pressure in the chamberincreases until the target growth pressure is reached. After reachingthe operating pressure, the chamber pressure may be periodically checkedand incrementally adjusted by releasing gas from the chamber to a ventline in order to keep the chamber pressure between, e.g., 124 kPa and125 kPa.

The growth temperature inside the heating apparatus and crucible may beincreased in two segments. For example, in the first segment, thetemperature is linearly increased from the room temperature to about1800° C. in 1.5 hours. Then, the second ramp segment to the final growthtemperature determined by the optical pyrometer, e.g. for 3.5 hours, maybe initiated after operator inspection.

The chamber is then maintained at the growth temperature and pressurefor a period of, for example, 1 hour. The drive apparatus 260 thenpushes the crucible 205 up at a rate ranging from about 0.2 to 1.0mm/hr, for example, at approximately 0.5 mm/hr. In a particular version,during the growth run, this push rate is held constant and the totaltravel is about 30 mm, producing a single crystal AlN boule that reachedabout 50 mm in diameter and 35 mm in length. Shorter or longer crystalsmay be produced by varying the distance the crucible 205 is pushed orequivalently by varying the push time.

Following completion of the vertical travel, the vertical motion of thecrucible 205 is stopped and the pressure is increased to 157 kPa byadding more high-purity forming gas. The power to the heating apparatusis then linearly reduced to zero, for example, in 6 hours and the systemis allowed to cool to room temperature. Following the cool down, thechamber is pumped to, e.g., less than about 1 mPa and backfilled toatmospheric pressure with forming gas. The chamber is then opened andthe growth crucible 205 removed for evaluation.

In various embodiments, after orienting the resulting single-crystalboule, e.g., by employing the x-ray Laue diffraction technique, theboule is encased in epoxy, e.g. VALTRON available from Valtech, and thenground down to a 25-mm diameter cylinder having its longitudinal axisoriented along the desired crystallographic direction. Once the orientedcylinder is produced, it is once again examined by the x-ray Lauediffraction technique to determine precise orientation (within +/−0.2°)and then sliced with a wire saw, e.g. the Model DT480 saw, for example,the one available from Diamond Wire Technologies, into a wafer. Thoseskilled in the art of semiconductor wafer preparation will readilyrecognize that there are many alternatives for slicing the crystal usingdiamond-coated ID and OD saws. The surface of the wafer is then preparedfor epitaxial growth utilizing, for example, one or more techniquesdescribed in the '838 patent.

Seeded Growth Using Polished Semiconductor Wafers

In some embodiments, a piece of semiconductor material (e.g., includingor consisting essentially of AlN) having a known crystallographicorientation is used as a seed from which bulk material may then begrown. In a particular embodiment, a polished AlN wafer sliced from abulk crystal is employed as a seed, offering a number of benefits,including standardization and improved control over the growthdirection.

In order to grow high-quality crystals, very high temperatures, forexample exceeding 2100° C., are generally desirable. At the same time,as discussed above, high axial thermal gradients are needed to providesufficient mass transport from the source material to the seed crystal.Additionally, non-zero radial thermal gradients, resulting in thermalgradient ratios less than 10 as detailed above, are preferably utilizedto enable growth of larger crystals at faster rates while maintaininghigh crystalline quality. However, if not chosen properly, these growthconditions may result in evaporation of seed material or its totaldestruction and loss.

Preferably, the mounting technique employed in these embodiments tosecure AlN seeds entails:

(1) employing a seed holder and/or adhesive compound that issufficiently strong to secure the seed and the crystal being grown;

(2) protecting the opposite side of the seed during growth to avoidre-evaporation of the AlN, as this may result in formation of planarand/or extended void defects; and

(3) avoiding contamination of the crystal and the crucible by thematerial chosen to protect the opposite side of the seed or as theadhesive.

In some embodiments, AlN seeded bulk-crystal growth is carried out inthe crucible 205 using a high-purity AlN source 230. In someembodiments, the apparatus 200 for growth of single-crystal AlN boulesincludes a crucible 205 such as the one disclosed in U.S. Pat. No.6,719,842 (the '842 patent), incorporated herein by reference in itsentirety, consisting essentially of tungsten and fabricated by a CVDprocess. Multiple grain layers within the wall of the crucible may beobtained by interrupting the tungsten deposition several times beforethe final wall thickness is obtained. Other crucible materials may beused, such as tungsten-rhenium (W—Re) alloys; rhenium (Re); tantalummonocarbide (TaC); a mixture of Ta₂C and TaC; a mixture of Ta₂C, TaC andTa; tantalum nitride (Ta₂N); a mixture of Ta and Ta₂N; hafnium nitride(HfN); a mixture of Hf and HfN; a mixture of tungsten and tantalum(W—Ta); tungsten (W); and combinations thereof. The apparatus preferablyhouses an AlN source material 230, for example, consisting essentiallyof high-purity AlN polycrystalline ceramic.

The tungsten crucible is placed into an inductively heated furnace, asdescribed above, so that the temperature gradient between the source 230and the seed crystal 235 drives vapor 225 to move from the hotter highpurity AlN ceramic source to the cooler seed crystal. The temperature atthe seed interface and the temperature gradients are monitored andcarefully adjusted, if necessary, in order to nucleate high-qualitymono-crystalline material on the seed and not destroy the AlN seed.Skilled artisans will also readily recognize that while variousembodiments of the present invention have been described herein asutilizing a seed crystal to promote crystal growth, the teachings hereinmay also be used for unseeded crystal growth, without departing from thescope and spirit of the present invention.

The terms and expressions employed herein are used as terms ofdescription and not of limitation, and there is no intention, in the useof such terms and expressions, of excluding any equivalents of thefeatures shown and described or portions thereof, but it is recognizedthat various modifications are possible within the scope of theinvention claimed.

1. A method of forming single-crystal aluminum nitride (AlN), the methodcomprising: condensing vapor comprising aluminum and nitrogen within agrowth chamber, thereby forming an AlN single crystal that increases insize along a growth direction; and thereduring, forming and maintaining,within the growth chamber, (i) a first non-zero thermal gradient in adirection substantially parallel to the growth direction and (ii) asecond non-zero thermal gradient in a direction substantiallyperpendicular to the growth direction, wherein a ratio of the firstthermal gradient to the second thermal gradient is less than
 10. 2. Themethod of claim 1, further comprising subliming solid source materialwithin the growth chamber to form the vapor.
 3. The method of claim 2,wherein the solid source material comprises polycrystalline AlN.
 4. Themethod of claim 1, wherein the second thermal gradient is larger than 4°C./cm.
 5. The method of claim 1, wherein the second thermal gradient issmaller than 85° C./cm.
 6. The method of claim 1, wherein the ratio ofthe first thermal gradient to the second thermal gradient is greaterthan 1.2.
 7. The method of claim 1, wherein the first thermal gradientis larger than 5° C./cm.
 8. The method of claim 1, wherein the firstthermal gradient is smaller than 100° C./cm.
 9. The method of claim 1,wherein the ratio of the first thermal gradient to the second thermalgradient is less than 5.5.
 10. The method of claim 1, wherein the ratioof the first thermal gradient to the second thermal gradient is lessthan
 3. 11. The method of claim 1, wherein forming the second thermalgradient comprises arranging a plurality of thermal shields outside thegrowth chamber.
 12. The method of claim 11, wherein each of the thermalshields comprises a refractory material.
 13. The method of claim 11,wherein each of the thermal shields comprises tungsten.
 14. The methodof claim 11, wherein each thermal shield defines an openingtherethrough.
 15. The method of claim 14, wherein the openings of thethermal shields are substantially equal in size to each other.
 16. Themethod of claim 14, wherein the opening of each thermal shield rangesfrom approximately 10 mm to approximately 2 mm less than a dimension ofthe growth chamber substantially perpendicular to the growth direction.17. The method of claim 14, wherein the openings of at least two of thethermal shields are different in size.
 18. The method of claim 17,wherein a first thermal shield having a first opening is disposedbetween the growth chamber and a second thermal shield, the secondthermal shield having a second opening larger than the first opening.19. The method of claim 11, wherein at least two of the thermal shieldshave different thicknesses.
 20. The method of claim 11, wherein athickness of each of the thermal shields ranges from approximately 0.125mm to approximately 0.5 mm.
 21. The method of claim 11, wherein thegrowth chamber comprises a lid disposed between the AlN single crystaland at least one of the thermal shields.
 22. The method of claim 21,wherein a thickness of the lid is less than approximately 0.5 mm. 23.The method of claim 21, wherein the lid comprises tungsten.
 24. Themethod of claim 1, further comprising disposing a seed within the growthchamber before forming the AlN single crystal, the AlN single crystalforming on the seed and extending therefrom in the growth direction. 25.The method of claim 24, wherein a diameter of the seed is greater thanapproximately 25 mm.
 26. The method of claim 1, wherein a growth rate ofthe AlN single crystal is greater than approximately 0.5 mm/hr.
 27. Themethod of claim 1, wherein the AlN single crystal forms on a seeddisposed within the growth chamber.
 28. A crystal-growth systemcomprising: a growth chamber for the formation of a single-crystalsemiconductor material via sublimation-recondensation therewithin alonga growth direction; a heating apparatus for heating the growth chamber;and a plurality of thermal shields arranged to form, within the growthchamber, (i) a first non-zero thermal gradient in a directionsubstantially parallel to the growth direction and (ii) a secondnon-zero thermal gradient in a direction substantially perpendicular tothe growth direction, wherein a ratio of the first thermal gradient tothe second thermal gradient is less than
 10. 29. The system of claim 28,wherein each thermal shield defines an opening therethrough.
 30. Thesystem of claim 29, wherein the openings of at least two of the thermalshields are different in size.
 31. The system of claim 30, wherein afirst thermal shield having a first opening is disposed between thegrowth chamber and a second thermal shield, the second thermal shieldhaving a second opening larger than the first opening.
 32. The system ofclaim 28, wherein at least two of the thermal shields have differentthicknesses.
 33. The system of claim 28, wherein a thickness of each ofthe thermal shields ranges from approximately 0.125 mm to approximately0.5 mm.
 34. The system of claim 28, wherein each of the thermal shieldscomprises a refractory material.
 35. The system of claim 28, whereineach of the thermal shields comprises tungsten.
 36. The system of claim28, wherein the thermal shields are arranged with substantially equalspacings therebetween.
 37. The system of claim 28, further comprising,disposed within the growth chamber, a seed for nucleating thesingle-crystal semiconductor material thereon.
 38. The system of claim37, wherein a diameter of the seed is greater than approximately 25 mm.39. The system of claim 37, wherein the seed comprises aluminum nitride.